where \(\mathbb {E}\)  denotes the underlying expectation. See [1]} for more information about martingale cotype. Pisier's famous renorming theorem asserts that \(X\)  is of martingale cotype \(q\)  iff \(X\)  admits an equivalent norm that is \(q\) -convex. Besides, he also proved that \(X\)  is of martingale cotype \(q\)  iff all \(X\) -valued Walsh-Paley martingales satisfy (REF ). See [2]} for more details.
